Selected topics in the history of the two-dimensional biharmonic problem

Author:

Meleshko VV1

Affiliation:

1. Department of Theoretical and Applied Mechanics, Kiev National Taras Shevchenko University, 01033 Kiev, Ukraine; meleshko@univ.kiev.ua

Abstract

This review article gives a historical overview of some topics related to the classical 2D biharmonic problem. This problem arises in many physical studies concerning bending of clamped thin elastic isotropic plates, equilibrium of an elastic body under conditions of plane strain or plane stress, or creeping flow of a viscous incompressible fluid. The object of this paper is both to elucidate some interesting points related to the history of the problem and to give an overview of some analytical approaches to its solution. This review article contains 758 references.

Publisher

ASME International

Subject

Mechanical Engineering

Reference897 articles.

1. Lame´ G (1859), Lec¸ons sur les coordonne´es curvilignes et leurs diverses applications, Mallet-Bachelier, Paris.

2. Jeffery GB (1920), Plane stress and plane strain in bipolar co-ordinates, Philos. Trans. R. Soc. London, Ser. A 221, 265–293.

3. Clebsch A (1883), The´orie de l’e´lasticite´ des corps solids, Dunod, Paris.

4. Boobnoff [Bubnov] IG (1902), On the stresses in a ship’s bottom plating due to water pressure, Trans. Inst. Naval Arch. 44, 15–46,

5. (1902), On the stresses in a ship’s bottom plating due to water pressure, 44, 47–52 (discussion).

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